find the coordinates of the missing endpoint given that p is the midpoint of NQ N(5,4) P(6,3) Q(3,9) P(-1,5)

Confusing: P(6,3), P(-1,5).

You have 2 points labeled "P".

To find the coordinates of the missing endpoint, we can use the midpoint formula.

The midpoint formula states that the coordinates of the midpoint between two points (x1, y1) and (x2, y2) are given by:

Midpoint = ((x1 + x2)/2, (y1 + y2)/2)

Let's use this formula to find the coordinates of the missing endpoint:

Given:
N(5, 4)
P(6, 3)
Q(3, 9)

Let the missing endpoint be R(x, y).

Using the midpoint formula, we have:

Midpoint(NP) = ((x + 6)/2, (y + 3)/2)

The midpoint between N(5, 4) and P(6, 3) is given as P(6, 3), so we can equate the coordinates:

(x + 6)/2 = 6 ... (1)
(y + 3)/2 = 3 ... (2)

Solving equation (1) for x:
x + 6 = 2 * 6
x + 6 = 12
x = 12 - 6
x = 6

Solving equation (2) for y:
y + 3 = 2 * 3
y + 3 = 6
y = 6 - 3
y = 3

Therefore, the missing endpoint R is at coordinates R(6, 3).

To find the coordinates of the missing endpoint, we can use the midpoint formula.

The midpoint formula states that the coordinates of the midpoint between two endpoints, (x1, y1) and (x2, y2), is given by the formula:

Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)

In this case, we know the coordinates of the midpoint P, which is (6, 3). We also know one of the endpoints N, which is (5, 4) or (-1, 5), and we need to find the missing endpoint Q.

Since N is an endpoint and P is the midpoint, we can use the midpoint formula to find the coordinates of Q.

Let's solve for Q using the endpoint (5, 4):

Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)
P = (6, 3)
N = (5, 4)

(6, 3) = ((5 + x2) / 2, (4 + y2) / 2)

Now, let's solve for the missing endpoint coordinates:

To find x2:
6 = (5 + x2) / 2
Multiply both sides by 2:
12 = 5 + x2
Subtract 5 from both sides:
7 = x2

To find y2:
3 = (4 + y2) / 2
Multiply both sides by 2:
6 = 4 + y2
Subtract 4 from both sides:
2 = y2

Therefore, the missing endpoint Q is (7, 2).

Note: If we had used the other endpoint (-1, 5), the calculations would be the same, and we would still get the same result of Q being (7, 2).

So, the coordinates of the missing endpoint Q are (7, 2).